LeetCode 235. Lowest Common Ancestor of a Binary Search Tree (二叉搜索树最近的共同祖先)
Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.
According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”
_______6______ / \ ___2__ ___8__ / \ / \ 0 _4 7 9 / \ 3 5
For example, the lowest common ancestor (LCA) of nodes 2
and 8
is 6
. Another example is LCA of nodes 2
and 4
is 2
, since a node can be a descendant of itself according to the LCA definition.
题目标签:Tree
这道题目给了我们一个二叉搜索树,和两个点,让我们找到这两个点的最近的共同祖先。什么是最近的共同祖先的呢?来看看题目给的例子,如果给的两个点是3和5, 那么它们的LCA就是4;如果给的是3和9,那么它们的LCA就是6。这道题目我们要根据BST的特性来做,BST的每一个点,它的左边的孩子都比它小,右边的孩子都比它大。
所以根据上述的这一点,我们每遍历一个点,就来判断一下要继续往左边走,还是往右边走,还是找到了祖先。
这里有三种情况:(对于每一个遍历点)
1. 拿p和q之间大的那一个 叫t-max, 和 遍历的点node比较一下,如果t-max 比node val 小的话,说明p和q 都在node 的左边,那么我们要继续走到左边取找;
2. 拿p和q之间小的那一个,t-min, 和遍历的点node比较一下,如果t-min 比node val 大的话,说明p和q都在node 的右边,那么我们要继续走到右边取找;
3. 剩下的情况就说明,p和q 在 node 的左右两边,或者是node 是p或者q, 另外一个点在node 的一边。 这种情况就是找到了祖先,把这一个node 返回。
Java Solution:
Runtime beats 62.62%
完成日期:07/04/2017
关键词:Tree (BST); LCA (lowest common ancestor)
关键点:只遍历左边或者右边根据BST的特性
1 /** 2 * Definition for a binary tree node. 3 * public class TreeNode { 4 * int val; 5 * TreeNode left; 6 * TreeNode right; 7 * TreeNode(int x) { val = x; } 8 * } 9 */ 10 public class Solution 11 { 12 13 14 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) 15 { 16 if(root == null) 17 return null; 18 19 // go into left child if the greater from p and q is smaller than root; 20 if(Math.max(p.val, q.val) < root.val) 21 return lowestCommonAncestor(root.left, p, q); 22 23 // go into right child if the smaller from p and q is greater than root; 24 if(Math.min(p.val, q.val) > root.val) 25 return lowestCommonAncestor(root.right, p, q); 26 27 // if p and q are not at the left side, and also not at the right side 28 // meaning p and q are at the both side or root is p or q , another one is at one side. 29 return root; 30 } 31 32 33 }
参考资料:
http://www.cnblogs.com/grandyang/p/4640572.html
LeetCode 算法题目列表 - LeetCode Algorithms Questions List